The present invention relates to key agreement protocols for transfer and authentication of encryption keys.
To retain privacy during the exchange of information it is well known to encrypt data using a key. The key must be chosen so that the correspondents are able to encrypt and decrypt messages but such that an interceptor cannot determine the contents of the message.
In a secret key cryptographic protocol, the correspondents share a common key that is secret to them. This requires the key to be agreed upon between the correspondents and for provision to be made to maintain the secrecy of the key and provide for change of the key should the underlying security be compromised.
Public key cryptographic protocols were first proposed in 1976 by Diffie-Hellman and utilized a public key made available to all potential correspondents and a private key known only to the intended recipient. The public and private keys are related such that a message encrypted with the public key of a recipient can be readily decrypted with the private key but the private key cannot be derived from the knowledge of the plaintext, ciphertext and public key.
Key establishment is the process by which two (or more) parties establish a shared secret key, called the session key. The session key is subsequently used to achieve some cryptographic goal, such as privacy. There are two kinds of key agreement protocol; key transport protocols in which a key is created by one party and securely transmitted to the second party; and key agreement protocols, in which both parties contribute information which jointly establish the shared secret key. The number of message exchanges required between the parties is called the number of passes. A key establishment protocol is said to provide implicit key authentication (or simply key authentication) if one party is assured that no other part aside from a specially identified second party may learn the value of the session key. The property of implicit key authentication does not necessarily mean that the second party actually possesses the session key. A key establishment protocol is said to provide key confirmation if one party is assured that a specially identified second party actually has possession of a particular session key. If the authentication is provided to both parties involved in the protocol, then the key authentication is said to be mutual; if provided to only one party, the authentication is said to be unilateral.
There are various prior proposals which claim to provide implicit key authentication.
Examples include the Nyberg-Rueppel one-pass protocol and the Matsumoto-Takashima-Imai (MTI) and the Goss and Yacobi two-pass protocols for key agreement.
The prior proposals ensure that transmissions between correspondents to establish a common key are secure and that an interloper cannot retrieve the session key and decrypt the ciphertext. In this way security for sensitive transactions such as transfer of funds is provided.
For example, the MTI/AO key agreement protocol establishes a shared secret K, known to the two correspondents, in the following manner.
1. During initial, one-time setup, key generation and publication is undertaken by selecting and publishing an appropriate system prime p and generator xcex1 of the multiplicative group Z*p, that is, xcex1xcex5Z*p; in a manner guaranteeing authenticity. Correspondent A selects as a long-term private key a random integer xe2x80x9caxe2x80x9d,1 less than a less than pxe2x88x921, and computes a long-term public key ZA=xcex1Z mod p. Correspondent B generates analogous keys b, zB. Correspondents A and B have access to authenticated copies of each other""s long-term public key.
2. The protocol requires the exchange of the following messages.
Axe2x86x92B:xcex1x mod pxe2x80x83xe2x80x83(1)
Axe2x86x92B:xcex1y mod pxe2x80x83xe2x80x83(2)
where x and y are integers selected by correspondents A and B respectively.
The values of x and y remain secure during such transmissions as it is impractical to determine the exponent even when the value of xcex1 and the exponentiation is known provided of course that p is chosen sufficiently large.
3. To implement the protocol the following steps are performed each time a shared key is required.
(a) A chooses a random integer x, 1xe2x89xa6xxe2x89xa6pxe2x88x922, and sends B message (1) i.e. xcex1x mod p.
(b) B chooses a random integer y, 1xe2x89xa6yxe2x89xa6pxe2x88x922; and sends A message (2) i.e. xcex1y mod p.
(c) A computes the key K=(xcex1y)azBx mod p.
(d) B computes the key K=(xcex1x)bzAy mod p.
(e) Both share the key K=xcex1bx+ay.
In order to compute the key K, A must use his secret key a and the random integer x, both of which are known only to him. Similarly B must use her secret key a and random integer y to compute the session key K. Provided the secret keys a,b remain uncompromised, an interloper cannot generate a session key identical to the other correspondent. Accordingly, any ciphertext will not be decipherable by both correspondents.
As such this and related protocols have been considered satisfactory for key establishment and resistant to conventional eavesdropping or man-in-the middle attacks.
In some circumstances it may be advantageous for an adversary to mislead one correspondent as to the true identity of the other correspondent.
In such an attack an active adversary or interloper E modifies messages exchanged between A and B, with the result that B believes that he shares a key K with E while A believes that she shares the same key K with B. Even though E does not learn the value of K the misinformation as to the identity of the correspondents 5 may be useful.
A practical scenario where such an attack may be launched successfully is the following. Suppose that B is a bank branch and A is an account holder. Certificates are issued by the bank headquarters and within the certificate is the account information of the holder. Suppose that the protocol for electronic deposit of funds is to exchange a key with a bank branch via a mutually authenticated key agreement. Once B has authenticated the transmitting entity, encrypted funds are deposited to the account number in the certificate. If no further authentication is done in the encrypted deposit message (which night be the case to save bandwidth) then the deposit will be made to E""s account.
It is therefore an object of the present invention to provide a protocol in which the above disadvantages are obviated or mitigated.
According therefore to the present invention there is provided a method of authenticating a pair of correspondents A,B to permit exchange of information therebetween, each of said correspondents having a respective private key a,b and a public key pApB derived from a generator a and respective ones of said private keys a,b, said method including the steps of
i) a first of said correspondents A selecting a first random integer x and exponentiating a function f(xcex1) including said generator to a power g(x) to provide a first exponentiated function f(xcex1)g(x);
ii) said first correspondent A generating a first signature sA from said random integer x and said first exponentiated function f(xcex1)g(x);
iii) said first correspondent A forwarding to a second correspondent B a message including said first exponentiated function f(xcex1)g(x) and the signature sA;
iv) said correspondent B selecting a second random integer y and exponentiating a function fxe2x80x2(xcex1) including said generator to a power g(y) to provide a second exponentiated function fxe2x80x2(xcex1)g(y) and a signature sB obtained from said second integer y and said second exponentiated function fxe2x80x2(xcex1)g(y);
v) said second correspondent B forwarding a message to said first correspondent A including said second exponentiated function fxe2x80x2(xcex1)g(y) and said signature sB.
vi) each of said correspondents verifying the integrity of messages received by them by computing from said signature and said exponentiated functioning such a received message a value equivalent to said exponentiated function and comparing said computed value and said transmitted value;
vii) each of said correspondents A and B constructing a session key K by exponentiating information made public by said other correspondent with said random integer that is private to themselves.
Thus although the interloper E can substitute her public key pE=xcex1ae in the transmission as: part of the message, B will use pE rather than pA when authenticating the message. Accordingly the computed and transmitted values of the exponential functions mill not correspond.